Finally, we constructed 6 value portfolios which are monthly rebalanced as momentum portfolios: “Winner 12x1”, “Loser 12x1”, “Winner-Loser 12x1”, “Winner 12x3”, “Loser 12x3”, “Winner-Loser (WML) 12x3”.

Overall, we generated 12 momentum and value test portfolios.

value strategy momentum

2.5 Combo portfolio construction

As we have discussed earlier in literature review there are two distinct approaches to construct a combined portfolio. It was decided to focus on the method originally proposed by C. Asness which is based on weighting momentum and value portfolios into a single one. We do not reject validity and success of the double ranking approach, though it does not suit for our sample. Screening stocks with both characteristics requires much larger sample of companies. Nowadays, it seems us impracticable to perform such ranking under current Russian stock market size due to its relative youth. Double ranking may result in higher return but higher volatility due to lower portfolio size. Perhaps, it can be a topic of the next research, but currently we apply the construction of combo portfolios which is simply based on the averaging of WML zero cost portfolios of value and momentum strategies. In particular, we form combination of 50% WML momentum, 50% WML value stocks for one and three month holding period, and perform other variations of weights. We rebalance portfolios each month as well as C. Asness did in his study. Overall, we construct 18 combinations for every variation of weight. In total, we formed 31 portfolios.

Table 4 represents the monthly average returns and standard deviations of combination portfolios. In the next chapter we will compare portfolio risk adjusted returns, analyze descriptive statistics and perform hypotheses testing.

2.6 Hypotheses and asset pricing models

In order to understand whether momentum and value effects are anomalies or fair premium for risk associated with each strategy, we have to estimate expected return for each portfolio relating to risk, and then test the hypothesis whether the difference between expected and actual returns is significant. The same logic we apply for testing combined portfolios. Overall, we have to test 31 portfolios.

It is widely accepted in academia to use CAPM model for estimation of fair returns. The only source of risk is systematic risk. The model is represented by the following expression: ??_??i???_??=??_pi+??_pi(??_?????_??), where Rpi-portfolio return, R_f - risk-free rate, which is equal to MIBOR Rm - market return, proxied by MICEX index, ??_pi - portfolio alpha, a measure of excess return, ??_pi - is the measure of sensitivity between asset and market. Thus, the premium correlated with portfolio risk forms from compensation for market risk, (?????????), which depends on to what extend portfolio traces the market movements, and from compensation above market premium, ??. The significance of constant shows abnormal return of tested momentum, value and combined strategies.

The second model we apply is dual-beta CAPM which allows investors to differentiate downside risk (risk of loss) from upside risk (gain), whereas regular beta cannot distinguish between such potentials for loss and gain. The dual-beta model does not assume that upside beta and downside betas are the same but actually calculates what the values are for the two betas, thus allowing investors to make better-informed investing decisions. The dual-beta CAPM model can thus be expressed as:

,

where D is a dummy variable, which takes the value of 1 when the market index return is positive and zero if negative.

Finally, we form 3 hypotheses to test:

H1: Momentum effect exists in 1 and 3 month perspective, and following the strategy can bring abnormal returns;

H2: Value effect exists in 1 and 3 month perspective, and following the strategy can bring abnormal returns;

H3: Combined portfolio can bring abnormal returns in 1 and 3 month perspective.

These hypotheses will be tested for each constructed portfolio. If any profitable momentum, value or combined strategies would are found via applying sign test for significance of difference (explained later), they would be further tested whether the findings could be explained by differences in risk using CAPM and dual-beta.

Chapter 3. Results of empirical analysis

3.1 Dealing with non-normal distributions

To begin with, let us look at the Table 1: Descriptive statistics of portfolio returns. The marked values of skewness and kurtosis are too large. It is clearly seen that not all portfolio returns are distributed normally. Usually, distribution is considered to be normal if it is symmetric, that is skewness is 0, and kurtosis is equal to 3. Thus, we cannot apply standard t-test as it is constructed for normally distributed data and in our case it would be invalid.

There are various methods to deal with non-normal data. One of the reasons for non-normal portfolio returns might be too many extreme values in a data set, in particular outliers. Let us look at the histogram of momentum winner portfolio with 1 month holding period (MOMW1).

It is clearly seen that distribution is skewed to the right due to outliers. However, we are not going to eliminate them, as those outliers can be identified as truly special causes of highly speculative stocks. Besides, we expected a little percentage of outliers. Moreover, according to Zephyr StatFacts http://www.styleadvisor.com/resources/statfacts/skewness “one would prefer positive skewness. However, in the real world few investments exhibit a positive skew". Therefore, one might seek investments with skew that is “less negative” than the alternatives”. All distributions of calculated portfolio returns, except vall3, are positively skewed. Thus, we are leaving the skewness unedited. Kurtosis measures the fatness of distribution tails. High kurtosis might imply higher probability that an event occurring is extreme in relation to portfolio returns distribution. Thus, the higher the kurtosis coefficient is above the normal level of 3, the more likely that future returns will be either extremely large or extremely small. In our case all distribution of portfolio returns are positive or called leptokurtic Investopedia explains: “If the past return data yields a leptokurtic distribution, the stock will have a relatively low amount of variance, because return values are usually close to the mean. Investors who wish to avoid large, erratic swings in portfolio returns may wish to structure their investments to produce a leptokurtic distribution.” http://www.investopedia.com/terms/l/leptokurtic.asp All our investments except one follow leptokurtic distribution, which is a positive sign as we found out. Overall, we did not make any corrections of portfolio distributions.

3.2 Testing the median returns for significance

Nevertheless, in order to test the significance of monthly mean returns, t-test is invalid and a different test should be performed. One can apply a one-sample sign test. It is a nonparametric alternative of the one-sample t-test because it does not require the data to come from a normally distributed population, as the t-test does. Using this test we can determine whether the median of a group differs from a specified value, which is equal to 0 in our case.

The median monthly period returns for all portfolios are represented in Table 2. It can be observed that profitability of portfolios hold for 3 months is higher than 1 month profitability. All pure portfolio median monthly returns are significant except for MWML3 portfolio and “loser” value portfolio for both holding periods. It should be noted that returns of momentum winners and losers for both holding period are much closer to each other than for value winners and loser portfolios. The reason for such difference may be that value effect is stronger than momentum effect if both are present at all. Besides, MWML1 is significant only at 10% level, which also provides us with information that zero-cost momentum strategies are unprofitable. We intend to test whether the findings can be explained by differences in risks. We cannot simply state that momentum effect is anomaly basing on poor significance of zero cost strategy. The thing is that loser momentum strategies can behave not as was expected due to the general upward trend prevailing in the market. A figure 3 represents cumulative returns of market and momentum strategy with 3 month holding period over the studied period of 15 years. It is clearly seen that both winner and loser portfolios outperform the market on average and follows its movements. Here are the correlations between the compared strategies and market: MOML3,Rm=0.49; MOMW3,Rm=0.30; MOMW3,MOML3=0.56. As we stated above alpha coefficient indicates the abnormal rate of return of our portfolio in excess of predicted returns by CAPM and dual-bets CAPM. Thus, we would still test momentum portfolios on the presence of abnormal return.

As the for profitability of combinations, all of medians are significantly different from 0. It is obvious, that median and mean returns of combo strategy will be within the interval form momentum returns to value returns, as we can observe that value outperforms momentum. Nevertheless, we cannot conclude yet whether value is better than momentum, or combination is outperforms both, until we calculate some widely used portfolio performance measures. Once we analyze the performance of our portfolios, then we will start the regression analysis of time series returns in order to estimate portfolio betas, alphas, check them for significance and finally conclude on solvency of tested hypotheses.

3.3 Performance measurement of constructed portfolios

There are several performance measure ratios which are commonly applied in modern portfolio management practice. These are Sharpe ratio, Treynor ratio, Jensen ratio (alpha) and information ratio. We would also estimate downside beta to capture the risk associated with potential for loss.

To begin with, it should be mentioned that performance is compared on an annualized basis. Therefore, we need to calculate annual returns of portfolios from monthly data using the following procedure. First, we found monthly arithmetic average for each year. Then, all values are multiplied by 12 to get annualized portfolio returns. To get average yearly returns for 15 years period we again simply take an arithmetic average. The obtained values for each strategy are represented in Table 3: Performance measure statistics.

The first performance ratio to be calculated is known as Sharpe ratio which measures performance in terms of both systematic and idiosyncratic risk. SR of portfolio is calculated as the excess return on investment divided by standard deviation of portfolio. To calculate the denominator, first we have to find standard deviation of returns for each year. To annualize standard deviation, we calculate standard deviations of each year from monthly values multiplied by the square root of 12. Then, the obtained figures are raised to the power of 2 in order to get yearly variances which are further summed and divided by 14 (15 years minus 1). The resulting values of variances for a sample of 15 years are raised to the power of Ѕ to get standard deviations.

Table 3 also represents these values for each strategy as well corresponding Sharpe ratios. The average value of 180 days-1year MIBOR (11.47%) is used for the studied period as a risk-free rate. The maximum SR (1.83) is attained by zero-cost value portfolio with 3-month holding return period, the minimum one (-0.3) is attained by loser value portfolio of the same holding period. The highest and lowest figures among combinations are 1.78 for 10/90 3-month period and -0.09 for 90/10 3-month period respectively, where the first weight stays for momentum strategy, the second for value strategy. It is clearly seen form the Table 3 that combined portfolios outperform pure zero-cost momentum but underperform pure zero-cost value portfolios if compare on the SR basis. However, we need to calculate some other ratios in order to make justified judgement on portfolios performance.

One more widely used ratio is Treynor ratio which measures the performance only in terms of systematic risk. TR is calculated as the portfolio excess return divided by portfolio beta. Again, we used yearly returns and calculated yearly betas as well simply as covariance of yearly returns of a certain portfolio and market divided by annualized market variance for the 15-year period. Also we have computed Jensen ratio and Modigliani risk-adjusted measure. The former is also known as alpha as we discussed previously, showing the abnormal return on investment, where the last is measured in units of per cent return and cab be calculated as the difference between Sharpe ratio of active and market portfolio multiplied by standard deviation of market return. All figures can be observed in Table 3.

The tendency is still the same: combo portfolios tend to outperform momentum portfolios but underperform value portfolios. There are negative betas for some portfolios meaning investment tend to decline when market rises, while increases when market falls. Only two portfolios have betas bigger than 1 (valw3 and valw1), while the rest have betas lower than 1. The lowest positive betas are 0.03 for 50/50-1 and 0.02 for 90/10-3, implying these portfolios are very defensive. However 90/10-3 has negative SR, which is not impressive. Overall, the strategies 30/70-1, 30/70-3, 50/50-1, 70/30-1, 70/30-3, can be considered as the most conservative strategies, due to they have relatively low betas, and thus are less exposed to market fluctuations.

We do not intend testing whether alphas and betas are significant or not, as 15 observations are not sufficient to explain the robustness of the model. Nevertheless, these figures provide us with some basic information about performance on annualized basis.

3.4 Regression analysis (CAPM)

Now we are going to run regression analysis in order to test the significance of constants (alpha), betas (measure of systematic risk) on monthly data, check the overall robustness of the models and finally conclude on significance of the studied strategies.

First, we applied standard CAPM model. We have performed regressions both with and without risk-free rate. Moreover, autocorrelation was examined in order to satisfy Gauss-Markov conditions. If Durbin-Watson (D-W) statistics is close to zero, then positive autocorrelation is present in the model. It can be eliminated by autoregressive transformation, adding new variable AR(1) into the regression equation. If D-W is still smaller than 2, then add AR(2). Once the D-W statistics is close to 2, we may claim that the problem of autocorrelation is solved.

Table 6 represents estimation output of regression analysis. To simplify our analysis we use only one macroeconomic factor represented by the rate of return of MICEX index. As the aim of our work is to detect the abnormal return (alpha) of studied strategies, there is no need to use a lot factors that may influence our portfolio returns. Since alpha is a measure of risk-adjusted return to a market index and shows the under- or outperformance compared to market, it is sufficient to use only one factor. Nevertheless, we may face the problem of poor R², meaning that market return is bad proxy for predicting returns. Let us discuss the main findings of regression analysis.

As can be seen from the Table 6, there is no evidence of abnormal returns of all momentum strategies applied, as the constants of each constructed momentum portfolios are insignificantly different from zero. Moreover, momentum strategies yield almost the same results for 1 and 3 month holding period. Figure 4 shows average annual returns of each portfolio over the studied period. It is clearly observed that portfolio mom12X3 and mom12x1 have similar pattern in returns. Figure 3 represents the cumulative returns over 15 years. Zero-cost momentum strategies are deeply below the market return. Thus, we can finally conclude, that momentum and contrarian affects are absent in Russian stock market as no abnormal return can be attained. Nevertheless, we can still compare results of winner and loser momentum portfolios with market return. As we can see from Figure 3, momentum winner and loser separately tend to outperform cumulative market return., If an investor had followed a strategy of taking a long position of winner momentum stocks starting in 2001, he would have gained more than simply copying the market over 15 years. In other words, we cannot claim that this strategy is unjustifiable only due to it does not produce abnormal return besides market premium. So, the performance of the strategy must be explained not only by alpha but also by premium for risk. The difference between portfolio return and the market return is known as arithmetic attribution. A table 7 represents the attributions for all constructed portfolios and corresponding alphas. It is clearly observed that attribution for winner momentum portfolios is larger than estimated alphas. Even though we found no evidence of momentum effect, we managed to construct portfolios momw1 and momw3 that outperform the market on average.

As for value portfolios, the results are more satisfactory. Table 6 reports that all alphas, except vall1, are significant, meaning that there is a value effect in Russian stock market. The largest alphas are achieved by valw3 (4.24%) and valw1 (3.22%). Zero-cost value strategies produce 3.86% and 3.21%. Looking at the Figure 3, zero-cost value cumulative returns are appreciably above the market and momentum zero-cost portfolio returns. Moreover, there are observed different from momentum portfolios patterns of average yearly value returns across 1 and 3 month holding period. Figure 4 shows that returns of 1 and 3 month value portfolios were declining from 2001 to 2003, then rising up to 2006. Value performs slightly better than momentum in 2008, bur worse in 2012. Both value zero-cost strategies benefit from diversification, as a result the average annualizes standard deviations obtained are 26.34% of vwml3 portfolio and 29.03% of vwml1, which are lower the market risk of 31.11%.

The combined portfolios were formed from weighting zero-cost value and momentum portfolios. Since we provided an argument for insignificance of momentum strategy, there is no rationale behind combining significant and insignificant strategies. But we are still interested whether such a combination can yield a higher risk-adjusted return than each separately. We also run a CAPM for combo portfolios and check their significance. Table 6 also represents the regression output for each combined portfolio. Portfolios 50/50(1), 50/50(3), 70/30(1), 30/70(1), 10/90(1), 10/90(3), 20/80(1), 20/80(3), 40/60(1), 40/60(3) and 60/40(3) produce positive significant alphas, meaning that combined strategies can bring abnormal return. These alphas are greater than momentum portfolio alphas, whereas lower than value portfolio alphas. Relating to Table 4, none of the combined portfolios outperform the value component separately analyzing different measures of performance. The potential of combined strategies to outperform value and momentum is solid diversification. As we can see form the Table 5, momentum and value strategies are negatively correlated implying that both strategies can offset each other during market disturbances. Thus, a combination of value and momentum portfolios can be considered as a hedging strategy.

3.5 Dual-beta CAPM

We performed dual-beta CAPM in order to check whether it has stronger explanatory power and estimate downside and upside betas. We report regression output only for zero-cost portfolios in Table 8 as the results obtained are not as expected. R² in most cases remained unchanged, but also decreased for some portfolios. The constants of momentum portfolios remain insignificant as well as under standard CAPM. Finally, estimated upside and downside betas are also insignificant.

3.6 Summary

On the grounds of conducted research, we may draw a conclusion of the strength of the raised hypotheses.

H1: Momentum effect exists in 1 and 3 month perspective, and following the strategy can bring abnormal returns.

The hypothesis is rejected as no evidence of momentum effect in Russian stock market found. However, the constructed winner portfolios with one and three month holding period, and based on the stock selection criteria of best past performance for previous 11 months skipping the recent month, has outperformed the market over the 15 year observation period. But still, the strategy failed to bring abnormal return.

H2: Value effect exists in 1 and 3 month perspective, and following the strategy can bring abnormal returns;

We do not reject the hypothesis, as there was found strong evidence of value effect in Russian stock market. The strategy generates significant positive alphas.

H3: Combined portfolio can bring abnormal returns in 1 and 3 month perspective.

Finally, we do not reject this hypothesis even though combined portfolios did not manage to outperform corresponding zero-cost value portfolios. Most of the combinations show significant abnormal return, outperforming market and separate momentum strategy.

Conclusion

The aim of this paper was to analyze the profitability of two distinct portfolio strategies and make a combination of them which would outperform both. We have investigated the Russian stock market for a period from Dec 2000 to May 2015 and have not found any evidence of momentum effect in Russian stock market. On the other hand, we have proved the presence of value effect, ability to generate abnormal profit taking long position in stocks with the lowest price-to-book ratio for the previous month and shorting stocks with the highest price-to-book ratio. Also, the combination of value and momentum strategies resulted in significant abnormal return but did not manage to outperform value strategy.

On the one hand, the results on momentum effect contradict to the previous research conducted on profitability of momentum strategies in Russian stock market by A. Maslovskaya for a period from January 1998 to April 2013, on the other hand, coincide with V. Ioffe's research for a period 1996-2009. We have not tried to explain such differences in results, probably, the transaction costs associated with frequent rebalancing that were took into account in Ioffe's research may born such discrepancy in results. Though, we did not consider the transaction costs at all, the findings are still indicating the absence of momentum effect in Russian stock market.

Further, we reported strong evidence of value effect. Following proposed value strategy based on sorting stocks by their price-to-book ratio, one can earn on average (over 15-year observation period) positive abnormal return in amount of 3.86% for zero-cost value strategy with 3 month holding period and 2.9% with 1 month holding period versus market return of 1.84% over the same period. Finally, 11 of 18 combinations managed to generate positive significant alphas and outperform the market over the studied period.

Further research of analyzed strategies may include the following issues. First, it would be reasonable to include brokerage commissions and income taxes, so the results may change. Secondly, the longer holding period for value strategy should be used, and value effect should be studied more deeply, as there are no enough researches on value strategy in Russia, while nowadays Russian stock market is considered very cheap and undervalued in comparison to developed markets. Thirdly, different techniques of screening stocks can be applied, for example, a 52-week highest price indicator for momentum and P/E ratio, current ratio, debt-to-equity ratio for value strategy. Moreover, it would be of particular interest to use a different style of forming combined portfolios. As we have mentioned before, the double ranking criteria may also be profitable strategy. In order to check it, a distinct research of momentum and value strategies should be done including all the recommendations above and then compare the resulting combination with the combination formed in our research. Finally, it is necessary to improve the CAPM specification, additional new factors, such as level of GDP, liquidity measures, or apply Fama-French three-factor model.

Bibliography

1. Andy Chui, Sheridan Titman, and John Wei, “Individualism and Momentum around the World” The Journal of Finance, Volume 65, Issue 1, pages 361-392, February 2010

2. Asness Clifford, "The interaction of value and momentum strategies", Financial Analysts Journal, 1997, pp. 29-36.

3. Athanassakos, G. “Value versus Growth Stock Returns and the Value Premium: The Canadian Experience 1985-2005”, 2009, Canadian Journal of Administrative Science, 26, p. 109-121.

4. Bauman, W. S., Conover, C. M., and Miller, R. E. “Growth versus Value and Large-Cap versus Small-Cap Stocks in International Markets”, 1998, Financial Analysts Journal, 54, p. 75-89.

5. Bekaert, Erb, Harvey, and Viskanta , “The behavior of emerging market returns”, 1997

6. Buffett, W. “The Superinvestors of Graham-and-Doddsville”, 1984, Hermes, p. 4-15.

7. Capaul, C., Rowley, I., and Sharpe, W. F. “International Value and Growth Stock Return”, 1993, Financial Analysts Journal, 49, p. 27-36.

8. Chan, L. K. C. and Lakonishok, J. “Value and Growth Investing: Review and Update”, 2004, Financial Analysts Journal, 60, p. 71-86.

9. Chen, N., and Zhang, F. “Risk and Return of Value Stocks”, 1998, Journal of Business, 71, 501-535.

10. Cheng, J. W. and Wu, H., 2010: The profitability of momentum trading strategies: Empirical evidence from Hong Kong. International Review of Economics & Finance, 19(4), 527-538.

11. Clifford S. Asness, Tobias J. Moskowitz, and Lasse Heje Pedersen, “Value and momentum everywhere”, Working Paper No. 80 Chicago Booth Paper No. 12-53, 72 p.

12. Daniel, Hirshleifer, Subrahmanyam, “Investor Psychology and Security Market Under- and Overreactions” The Journal of Finance Volume 53, Issue 6, December 1998, pages 1839-1885.

13. DE Bondt, W.F.M. & Thaler, R.H. “Does the Stock Market Overreact?” Journal of Finance, 40, 1985, p. 793-805

14. Du, D., Huang, Zh., Liao, B., “Why is there no momentum in the Taiwan stock market?”, Journal of Economics and Busines 61, 2009, p. 140.

15. Fama, E. F., and French, K. R. “Multifactor Explanations of Asset Pricing Anomalies”, 1996, The Journal of Finance, 51, p. 55-84.

16. Graham, B. “A Conversation with Benjamin Graham”, 1976, Financial Analysts Journal, 32, p. 20-23.

17. http://extranet.datastream.com/data/Exchange%20&%20Interest%20Rates/RiskFreeInterestRates.htm

18. http://www.investopedia.com/terms/l/leptokurtic.asp

19. http://www.styleadvisor.com/resources/statfacts/skewness

20. James O'Shaughnessy, Patrick O' Shaughnessy, “The top stock-market strategy of the past 50 years”, marketwatch.com, Dec 16, 2011

21. Jegadeesh and Titman, “Returns to Buying Winners and selling losers: implication for stock market efficiency”, Journal of Finance, Volume 48, Issue 1, March 1993, p. 65-91.

22. Jim Fink, “So, You Want to Be a Value Investor? - Think Businesslike”, Investingdaily.com

23. Jim Fink, “The Holy Grail of Investing: Combining Value and Momentum”, investingdaily.com

24. John M. Griffin, Xiuqing Ji , J. Spencer Martin, “Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole” The Journal of Finance, 58, Issue 6, December 2003 p. 2515-2547,

25. K. Terentyev, “Predicting returns with accounting ratios in Russian stock market”, 2014.

26. Kouwenberg and Salomons, “Value investing in emerging markets: local macroeconomic risk and extrapolation”, 2003, 30 p.

27. Lakonishok, J., Shleifer, A., and Vishny, R. W. “Contrarian Investment, Extrapolation, and Risk”, 1994, the Journal of Finance, 49, p. 41-78.

28. Luis Berggruna and Oliver Rauscha, “Momentum in the Colombian Stock Market”, Latin American Business Review, Volume 12, Issue 1, p. 1-23 , 2011.

29. A. Maslovskaya, “Liquidity role in explanation of momentum effect in Russian stock market”, HSE, 2013.

30. Muga, Santamaria “Momentum Effect in Latin American Emerging Markets”, Emerging Markets Finance and Trade, Vol. 43,No. 4, pp. 25-46, July-August 2007 .

31. Narasimhan Jegadeesh, Sheridan Titman “Returns to Buying Winners and selling losers: implication for stock market efficiency”, Journal of Finance, Volume 48, Issue 1, March 1993, p. 65-91.

32. Oppenheimer, H. R. “A Test of Ben Graham's Stock Selection Criteria”, `984 Financial Analysts Journal, 40, p. 68-74.

33. Robert A. Levi, “Relative strength as a criterion for investment selection”, , Journal of Finance, 22, Issue 4, 1967, p. 595-610

34. Rouwenhorst, K.G., “International Momentum Strategies”, Journal of Finance 53, 1998, p. 267.

35. Rozeff, M. S., and Zaman, M. A. “Overreaction and Insider Trading: Evidence from Growth and Value Portfolios”, 1998, The Journal of Finance, 53, p. 701-716.

36. Vladimir Ioffe, “Return based investment strategies on the Russian stock market: the empirical study”, Copenhagen Business School, 2010.

Appendix

Figure 1: Number of companies

Figure 2: Monthly total returns

market

mwml1

mwml3

vwml1

vwml3

Figure 3: Cumulative returns over 15-year observation period

Figure 4: Annual returns of portfolios

Figure 5: Distribution of returns



Table 1: Descriptive statistics of portfolio returns.

The marked values seemed us suspicious at first sight. But most of the high kurtosis and skewness are caused by extreme outliers which are a normal case for a stock market, especially developing one, since there would also be outstanding leaders and deep laggards. So, we have not laid special emphasis to the portfolios with these high values. But we take into account for using a one-sample sign test instead of simple t-test.

Portfolio/Stat	Mean	Median	Maximum	Minimum	Std. Dev.	Skewness	Kurtosis
MOMW1	0.022558	0.01451	0.699104	-0.23991	0.0998	3.29354	23.5602
MOML1	0.015508	0.01056	0.327599	-0.335854	0.0867	0.18524	6.17784
MOMWML1	0.007049	0.00830	0.795	-0.293	0.0993	3.36115	30.6105
MOMW3	0.022941	0.01683	0.667823	-0.241709	0.0877	2.31887	19.1239
MOML3	0.016143	0.01115	0.201382	-0.182951	0.0634	0.00097	4.39190
MOMWML3	0.006798	0.00772	0.559859	-0.166918	0.0762	2.17890	18.3764
VALW1	0.048665	0.02570	0.799513	-0.324442	0.1260	2.368408	14.04695
VALL1	0.008034	0.00423	0.575468	-0.245828	0.0831	1.84746	15.1491
VALWML1	0.050137	0.02325	0.597344	-0.097205	0.0837	2.36840	14.04
VALW3	0.055510	0.02786	0.684458	-0.156722	0.1036	2.151915	11.4606
VALL3	0.017751	0.00324	0.435111	-0.516477	0.1502	-0.16093	4.46520
VALWML3	0.037765	0.03272	0.649039	-0.290817	0.1178	1.255273	8.36423
COM50/50(1)	0.028593	0.01578	0.900256	-0.161370	0.0908	5.793919	52.35898
COM50/50(3)	0.026352	0.02140	0.348761	-0.123961	0.0681	0.937620	6.79122
COM70/30(1)	0.030003	0.01743	0.915696	-0.220034	0.1029	4.791507	38.3114
COM70/30(3)	0.017053	0.014975	0.228649	-0.129946	0.0579	0.298802	4.57072
COM30/70(1)	0.030618	0.01911	0.413278	-0.108590	0.0630	1.98456	10.99423
COM30/70(3)	0.035671	0.02357	0.485401	-0.072657	0.0604	3.49	22.55012

Table 2: Sign test (normal approximation)

% return is median monthly return, as median is better suited for skewed distributions to derive at central tendency since it is much more robust and sensible.

Strategy/type	Winner	Loser	WML
	% return	value	% return	value	% return	value
MOM1	1.45%	2.28**	1.06%	2.45**	0.083%	1.67***
MOM3	1.68%	3.04*	1.11%	2.89*	0.077%	1.22
VAL1	2.57%	4.56*	0.042%	0.91	2.32%	4.41*
VAL3	2.78%	6.65*	0.032%	0.15	3.27%	3.98*
Combination	1 month	3 months
50mom/50val	1.57% (3.95*)	2.14% (4.43*)
70mom/30val	1.74% (3.95*)	1.49% (3.60*)
30mom/70val	1.90% (4.95*)	2.35% (7.74*)

*^{-1% significance level;} **^{-5% significance level;} ***^{-10% significance level.}

Table 3: Performance measure statistics (yearly)

Reported are the average returns, standard deviation of returns, Sharpe ratio (SR), beta of portfolio, Treynor ratio (TR), Jensen ratio (alpha), Modigliani risk-adjusted ratio (M²) for each constructed momentum, value and combined strategies in Russian stock market over a studied period 2001-2015. Each portfolio is sorted as W-winner, L-loser and WML as zero cost portfolio (winner minus loser). Statistics are computed from monthly return series but are reported as annualized numbers. Average 180 days-1year MIBOR of 11.47% is used in calculations of ratios.

	Return	Std. Dev.	SR	вp	TR	Alpha	M2
Market	22,19%	31,11%	0,34	1,00	0,11	0,00%	0,00%
MOMW3	27,92%	29,73%	0,55	0,746	0,22	8,45%	6,49%
MOML3	19,52%	19,97%	0,40	0,75	0,11	0,01%	1,82%
MWML3	8,40%	26,41%	-0,12	-0,004	7,29	-3,03%	-14,35%
MOMW1	26,21%	34,61%	0,43	0,64	0,23	7,86%	2,52%
MOML1	20,36%	30,38%	0,29	0,91	0,10	-0,87%	-1,63%
MWML1	5,86%	36,34%	-0,15	-0,27	0,21	-2,74%	-15,53%
VALW3	66,42%	31,46%	1,75	1,21	0,46	42,02%	43,60%
VALL3	6,73%	15,99%	-0,30	0,53	-0,09	-10,46%	-19,94%
VWML3	59,68%	26,34%	1,83	0,67	0,72	41,00%	46,22%
VALW1	44,72%	30,97%	1,07	1,10	0,30	21,48%	22,68%
VALL1	8,66%	27,92%	-0,10	0,77	-0,04	-11,05%	-13,85%
VWML1	36,06%	29,03%	0,85	0,33	0,75	21,06%	15,62%
50/50(x1)	20,96%	21,86%	0,43	0,03	3,10	9,16%	2,78%
50/50(x3)	31,87%	17,52%	1,16	0,31	0,66	17,09%	25,49%
70/30(x1)	22,13%	27,74%	0,38	-0,02	-4,62	10,91%	1,23%
30/70(x1)	27,00%	21,89%	0,71	0,15	1,03	13,92%	11,35%
70/30(x3)	20,74%	17,64%	0,53	0,16	0,57	7,53%	5,63%
30/70(x3)	25,95%	22,07%	0,66	0,21	0,70	12,25%	9,68%
10/90 (1)	33,04%	25,95%	0,83	0,27	0,80	18,68%	15,13%
10/90 (3)	54,12%	23,89%	1,78	0,60	0,71	36,22%	44,80%
20/80 (1)	30,02%	23,49%	0,79	0,21	0,88	16,30%	13,83%
20/80 (3)	48,56%	21,70%	1,71	0,53	0,70	31,44%	42,44%
40/60 (1)	23,98%	21,31%	0,59	0,09	1,39	11,54%	7,53%
40/60 (3)	37,43%	18,41%	1,41	0,38	0,68	21,87%	33,14%
60/40 (1)	17,94%	23,45%	0,28	-0,03	-2,22	6,78%	-2,14%
60/40 (3)	26,31%	17,26%	0,86	0,24	0,63	12,31%	16,02%
80/20 (1)	11,90%	28,96%	0,01	-0,15	-0,03	2,02%	-10,27%
80/20 (3)	15,18%	18,64%	0,20	0,09	0,41	2,75%	-4,53%
90/10 (1)	8,88%	32,49%	-0,08	-0,21	0,12	-0,36%	-13,21%
90/10 (3)	9,62%	20,15%	-0,09	0,02	-1,10	-2,03%	-13,58%

Table 4: Monthly performance (% mean returns)

A figure in parentheses is a holding period (1 and 3 months) Monthly Average MIBOR=0.96%

portfolio	% return	std. dev.	SR	M2
market	1,84%	8,92%	0,10	0,00%
50/50(1)	1,77%	6,10%	0,13	0,31%
50/50(3)	2,64%	5,15%	0,33	2,03%
70/30(1)	1,91%	7,72%	0,12	0,22%
30/70(1)	2,20%	6,11%	0,20	0,93%
70/30(3)	1,71%	5,05%	0,15	0,45%
30/70(3)	3,68%	7,69%	0,35	2,28%
10/90 (1)	2,62%	7,18%	0,23	1,18%
10/90 (3)	4,49%	7,44%	0,47	3,35%
20/80 (1)	2,41%	6,53%	0,22	1,10%
20/80 (3)	4,03%	6,69%	0,46	3,21%
40/60 (1)	1,98%	5,96%	0,17	0,65%
40/60 (3)	3,10%	5,51%	0,39	2,59%
60/40 (1)	1,56%	6,52%	0,09	-0,06%
60/40 (3)	2,17%	4,99%	0,24	1,29%
80/20 (1)	1,13%	7,99%	0,02	-0,69%
80/20 (3)	1,24%	5,32%	0,05	-0,41%
90/10 (1)	0,92%	8,93%	0,00	-0,92%
90/10 (3)	0,78%	5,77%	-0,03	-1,16%
MOMW3	2,29%	8,80%	0,15	0,47%
MOML3	1,61%	6,36%	0,10	0,03%
MWML3	0,68%	6,39%	-0,04	-1,27%
MOMW1	2,26%	10,04%	0,13	0,27%
MOML1	1,55%	8,70%	0,07	-0,27%
MWML1	0,70%	9,96%	-0,03	-1,11%
VALW3	5,45%	10,41%	0,43	2,97%
VALL3	0,59%	5,05%	-0,07	-1,53%
VWML3	4,96%	8,25%	0,49	3,45%
VALW1	3,64%	9,20%	0,29	1,72%
VALL1	0,80%	8,34%	-0,02	-1,05%
VWML1	2,84%	8,00%	0,24	1,22%

Table 5: Correlation matrix

Portfolio	MWML1	MWML3	VWML1	VWML3
MWML1	1	0,62949207	-0,34755314	-0,34345412
MWML3	0,62949207	1	0,107427772	-0,16572395
VWML1	-0,34755314	0,107427772	1	0,450595721
VWML3	-0,34345412	-0,16572395	0,450595721	1

Table 6: Regression analysis output (CAPM)

Подобные документы

• Post-Modern Portfolio Theory

  The core innovation of post-modern portfolio theory. Total variability of return. Downside risk optimization. Downside frequency, average deviation and magnitude. Main types of formulas for downside risk. Main features of the Sortino and Sharpe ratio.
  
  реферат [213,9 K], добавлен 15.12.2012
  

• Pipeline capacity and economics

  Gas pipeline construction: calculating the pipe diameter, the pressure required for the transportation of natural gas compressors. The definition of capital costs for construction and operation of the pipeline. Financial management of the project.
  
  статья [774,7 K], добавлен 05.12.2012
  

• Transfer Pricing

  Special features of multinational corporations. Out the main objectives of a transfer pricing system. Modernisation of business processes of enterprise, use of innovative technologies. Preparing the profit and loss account of the company of Crystal ltd.
  
  курсовая работа [28,6 K], добавлен 16.02.2014
  

• The Fast-food Industry: McDonald’s, Burger King, Wendy’s, Hardee’s and White Castle

  The Hamburger Industry: franchising, market conduct, marketing strategies of competing parties. Challenges confronting in the fast-food industry. Conflicts between franchisers and franchisees. Consumer behavior. The main role of management, its changes.
  
  курсовая работа [29,7 K], добавлен 06.11.2013
  

• Electronic Construction Procurement System

  Project background and rationales. Development methodology, schedule planning. Company mission and vision. Organization of staff and company structure. Procurement system target market. Implementation of procurement system. Testing, user manual.
  
  дипломная работа [6,8 M], добавлен 28.11.2013
  

• Alcohol influence on economics-related decision-making

  The experiments related to alcohol and economic decision-making. First study attempting to test 3 sets of embedded hypotheses regarding how alcohol influences our choices. Conducting games, showing the effects of alcohol on the decision-making process.
  
  статья [268,5 K], добавлен 04.11.2015
  

• САРМ и его значение

  База для распространенной практики пассивного инвестирования. Формирование и поддержание диверсифицированного портфеля ценных бумаг. Оценка ставок доходности. Расчет ценовой модели акционерного капитала при помощи САРМ (Capital Assets Pricing Model).
  
  презентация [257,8 K], добавлен 15.10.2011
  

• Модель арбитражного ценообразования (Arbitrage Pricing Theory, APT)

  Понятие арбитража как получения безрисковой прибыли от сделок на разнице цен. Совершение сделок на разных рынках с одинаковыми товарами или финансовыми активами. Характеристика моделей САРМ и АРТ, основные присущие им факторы. Оценка премии за риск.
  
  презентация [11,5 K], добавлен 30.07.2013
  

• Comprehensive analysis of the economic activity of the company "Turboatom"

  Directions of activity of enterprise. The organizational structure of the management. Valuation of fixed and current assets. Analysis of the structure of costs and business income. Proposals to improve the financial and economic situation of the company.
  
  курсовая работа [1,3 M], добавлен 29.10.2014
  

• The improvement of Russia’s investment climate: problems and perspectives

  Establishing a favorable environment for investments, removing administrative barriers. Establishing high-technology parks. Formation of financial mechanisms to attract and support investments, tax stimulation measures. Brand promotion of Russian regions.
  
  реферат [15,9 K], добавлен 04.06.2013
  

• Economy of Kazakhstan

  A variety of economy of Kazakhstan, introduction of the international technical, financial, business standards, the introduction to the WTO. The measures planned in the new Tax code. Corporation surtax. Surtax reform. Economic growth and development.
  
  реферат [27,2 K], добавлен 26.02.2012
  

• How competitive is Russian economy?

  Concept of competitiveness and competition, models. Russia’s endowment. Engendered structural dominance and performance. The state of Russian competitiveness according to the Global Competitiveness Index. Place in the world, main growth in detail.
  
  курсовая работа [1,2 M], добавлен 28.05.2014
  

• Market and its Functioning

  Law of demand and law of Supply. Elasticity of supply and demand. Models of market and its impact on productivity. Kinds of market competition, methods of regulation of market. Indirect method of market regulation, tax, the governmental price control.
  
  реферат [8,7 K], добавлен 25.11.2009
  

• Stabilization policy: macroeconomic dimensions

  Models and concepts of stabilization policy aimed at reducing the severity of economic fluctuations in the short run. Phases of the business cycle. The main function of the stabilization policy. Deviation in the system of long-term market equilibrium.
  
  статья [883,7 K], добавлен 19.09.2017
  

• Разработка интегрированной системы управления отделением разваривания на спиртзаводе на основе программируемого логического контроллера Modicon TSX Momentum

  Автоматизация технологического процесса разваривания на спиртзаводе. Современная платформа автоматизации TSX Momentum. Программное обеспечение логического контроллера. Спецификация приборов, используемых в технологическом процессе пищевого производства.
  
  дипломная работа [8,7 M], добавлен 19.03.2014
  

• Alternative construction methods

  It is a try to examine some alternative methods in construction. Adobe construction is one of the oldest forms of building technology. A method of similar to rammed-earth is cast earth. A create monolithic walls of earth. Industial Construction Materials.
  
  контрольная работа [777,2 K], добавлен 18.07.2009
  

• В помощь аттестующимся. Из личного опыта

  Алгоритм и схема написания самоанализа как основного структурного элемента подготовки к аттестации педагогических работников. Анализ содержания блоков педагогической деятельности. Блочная система как один из вариантов оформления методического portfolio.
  
  методичка [5,1 M], добавлен 20.05.2009
  

• Planning a four-storey residential building

  Characteristics of the plot and area for reconstruction with the addition of the attic floor of a public building on Slastiona Street 3 in Lviv. Construction of the architectural part. List of mounting elements in the construction of the building.
  
  дипломная работа [2,0 M], добавлен 04.06.2022
  

• Спекулятивные стратегии на валютном рынке

  Исследование распространенных спекулятивных стратегий на валютах – carry, momentum, и value с точки зрения российского инвестора, который получает доходность в рублях. Кэрри-трейд и портфель из валют. Принципы построения портфеля и валютных стратегий.
  
  дипломная работа [397,0 K], добавлен 30.11.2016
  

• Portfolio-анализ как инструмент стратегического планирования маркетинга

  Назначение стратегического планирования маркетинга. Проведение Portfolio-анализа для гипотетической фирмы "Полиграфист". Конкурентоспособность и относительные доли рынка, занимаемые компанией. Построение матричных моделей General Electric-МсKinsey и BCG.
  
  курсовая работа [1,9 M], добавлен 01.05.2011
  

• главная
• рубрики
• по алфавиту
• вернуться в начало страницы
• вернуться к началу текста
• вернуться к подобным работам

Strategy	CAPM	Constant	Beta	AR(1)	D-W	R-squared
MOMW3	without rf	0.012649**	0.560306*	-	1.180694	0.322291
	AR(1)	0.010195***	0.439452*	0.268388*	2.182692	0.444772
	with rf	0.008455	0.551265*	-	1.178916	0.365640
	AR(1)	0.004766	0.436557*	0.267726*	2.101160	0.436781
MOML3	without rf	0.011162*	0.271134*	-	1.215778	0.144521
	AR(1)	0.013920	0.061702	0.552734*	2.151370	0.348241
	with rf	0.004183	0.260341*	-	1.244288	0.222403
	AR(1)	0.004880	0.058080	0.547283*	2.146178	0.474981
MWML3	without rf	0.001486	0.289172*	-	1.365923	0.113763
	AR(1)	-0.001742	0.269384*	0.161103*	2.055748	0.142874
	with rf	-0.005351	0.282216*	-	1.365919	0.201251
	AR(1)	-0.008825	0.269084*	0.167465*	2.029286	0.356852
MOMW1	without rf	0.013101**	0.514780*	-	1.416102	0.210081
	AR(1)	0.010788	0.407820*	0.194646*	2.117832	0.255635
	with rf	0.008445	0.508257*	-	1.398901	0.267324
	AR(1)	0.005056	0.405458	0.260515*	2.078007	0.357976
MOML1	without rf	0.002882	0.687336*	-	1.872735	0.495530
	AR(1)	0.003146	0.670893*	0.071170	1.952093	0.494479
	with rf	-0.000104	0.680829*	-	1.897666	0.532205
	AR(1)	-	-	0.055307	-	-
MWML1	without rf	0.010222	-0.172557	-	1.640109	0.023851
	AR(1)	0.007610*	-0.231606	0.081723	1.994987	0.058175
	with rf	-0.001075	-0.181280**	-	1.624970	0.025618
	AR(1)	-0.004262	-0.235334*	0.094169	1.982615	0.060286
VALW3	without rf	0.047798*	0.426472*	-	1.235004	0.133106
	AR(1)	0.049901*	0.259964*	0.430859*	2.199058	0.277917
	with rf	0.042375*	0.417775*	-	1.255237	0.179773
	AR(1)	0.042899*	0.255923*	0.428797*	2.208918	0.324480
VALL3	without rf	0.001257	0.257468*	-	0.746178	0.207685